# Nonlinear Stochastic Dynamics of Complex Systems, III: Noneqilibrium Thermodynamics of Self-Replication Kinetics

Source: [Nonlinear Stochastic Dynamics of Complex Systems, III: Noneqilibrium Thermodynamics of Self-Replication Kinetics](<https://www.sota2.com/research/paper/68fa350a1e209131ce89e2cf>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T21:02:06.700Z

Authors: David B. Saakian, Hong Qian

Published: 2016-06-08T04:17:57.000Z

## Abstract

We briefly review the recently developed, Markov process based isothermal chemical thermodynamics for nonlinear, driven mesoscopic kinetic systems. Both the instantaneous Shannon entropy {\\boldmath $S\[p\_{\\alpha}(t)\]$} and relative entropy {\\boldmath $F\[p\_{\\alpha}(t)\]$}, defined based on probability distribution {\\boldmath $\\{p\_{\\alpha}(t)\\}$}, play prominent roles. The theory is general; and as a special case when a chemical reaction system is situated in an equilibrium environment, it agrees perfectly with Gibbsian chemical thermodynamics: {\\boldmath $k\_BS$} and {\\boldmath $k\_BTF$} become thermodynamic entropy and free energy, respectively. We apply this theory to a fully reversible autocatalytic reaction kinetics, represented by a Delbr\\"{u}ck-Gillespie process, in a chemostatic nonequilibrium environment. The open, driven chemical system serves as an archetype for biochemical self-replication. The significance of {\\em thermodynamically consistent} kinetic coarse-graining is emphasized. In a kinetic system where death of a biological organism is treated as the reversal of its birth, the meaning of mathematically emergent "dissipation", which is not related to the heat measured in terms of {\\boldmath $k\_BT$}, remains to be further investigated.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1606.02391>)

[PDF](<https://arxiv.org/pdf/1606.02391.pdf>)